Question

1. Suppose X~N(0,1), what is Pr (X< -1.96)

2. Suppose X~N(0,1), what is Pr (1.20 <X<1.96)

3. Suppose X~N(0,1), what is Pr ( -1.96<X< 1.20)

Please use step by step work. I'm struggling to grasp the concepts. Thank you.

Answer 1

µ = 0, σ = 1

1. P(X < -1.96) =

= P( (X-µ)/σ < (-1.96-0)/1 )

= P(z < -1.96)

Using excel function:

= NORM.S.DIST(-1.96, 1)

= 0.025

-------------------

2.

P(1.20 < X < 1.96) =

= P( (1.20-0)/1 < (X-µ)/σ < (1.96-0)/1 )

= P(1.20 < z < 1.96)

= P(z < 1.96) - P(z < 1.2)

Using excel function:

= NORM.S.DIST(1.96, 1) - NORM.S.DIST(1.2, 1)

= 0.0901

-----------------

3.

P(-1.96 < X < 1.2) =

= P( (-1.96-0)/1 < (X-µ)/σ < (1.2-0)/1 )

= P(-1.96 < z < 1.2)

= P(z < 1.2) - P(z < -1.96)

Using excel function:

= NORM.S.DIST(1.2, 1) - NORM.S.DIST(-1.96, 1)

= 0.8599